In ΔKLM, l = 820 cm, m = 560 cm and ∠K=169°. Find the length of k, to the nearest centimeter.

Grace has drawn a Scalene and Obtuse triangle.

Triangles are classified according to the sides and according to the angles.

According to the length of sides there are three types of triangles.

According to the measurement of angles there are three types.  

So according to both the classification, the triangle Grace drew is a Scalene and an Obtuse triangle.

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The probability that the T-shirt John picks is dark blue is 2/3.

To find the probability that John picks a dark blue T-shirt, we'll need to consider the total number of blue T-shirts and the number of dark blue T-shirts.
Determine the total number of blue T-shirts.
John has 2 dark blue and 1 light blue T-shirt, so he has a total of 2 + 1 = 3 blue T-shirts.
Determine the number of dark blue T-shirts.
John has 2 dark blue T-shirts.
Calculate the probability.
The probability that John picks a dark blue T-shirt is the number of dark blue T-shirts divided by the total number of blue T-shirts.
Probability = (Number of dark blue T-shirts) / (Total number of blue T-shirts) = 2 / 3.

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Sothe non-parametric equation of the plane with the given normal vector and passing through the point (5, -6, 0) is: -5x + 6y + 6z + 61 = 0

In order to find the non-parametric equation of the plane, we need the normal vector and a point on the plane. The normal vector is given as (-5, 6, 6), and a point on the plane is (5, -6, 0).

The non-parametric equation of a plane is given by:

Ax + By + Cz = D

where (A, B, C) is the normal vector and (x, y, z) is a point on the plane. We can substitute the values into the equation to find the values of A, B, C, and D.

(-5)(x - 5) + (6)(y + 6) + (6)(z - 0) = 0

Expanding this equation:

-5x + 25 + 6y + 36 + 6z = 0

-5x + 6y + 6z + 61 = 0

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The lines "a" and "b" shown in the picture are parallel and crossed by a transversal line.

The angle that measures 65º and the adjacent angle to the one that measures (x+72)º are corresponding angles, which means that they are congruent.

Both adjacent angles are supplementary, which means that they add up to 180º

From this expression, you can determine the value of x, first, take the parentheses away and add the like terms:

Next, subtract 137 from both sides of the equation:

The value of x is 43 and the measure of the given angle is:

x+72 = 43+72 = 115º

Answer:

8.6

Step-by-step explanation:

In order to calculate the time it will take for Andrew to settle the loan, we can use the formula for compound interest. So, it will take Andrew approximately 5.22 years to settle the loan.

The formula is given as A = P(1 + r/n)^(nt), Where: A = the final amount, P = the principal (initial amount borrowed), R = the annual interest rate, N = the number of times the interest is compounded in a year, T = the time in years.

We know that Andrew borrowed R200 000 from a bank at an annual interest rate of 5.25% compounded quarterly and that he will make repayments of R6 000 at the end of every 3 months.

Since the first repayment will be made 3 months from now, we can consider that the initial loan repayment is made at time t = 0. This means that we need to calculate the value of t when the total amount repaid is equal to the initial amount borrowed.

Using the formula for compound interest: A = P(1 + r/n)^(nt), We can calculate the quarterly interest rate:r = (5.25/100)/4 = 0.013125We also know that the quarterly repayment amount is R6 000, so the amount borrowed minus the first repayment is the present value of the loan: P = R200 000 - R6 000 = R194 000

We can now substitute these values into the formula and solve for t: R194 000(1 + 0.013125/4)^(4t) = R200 000(1 + 0.013125/4)^(4t-1) + R6 000(1 + 0.013125/4)^(4t-2) + R6 000(1 + 0.013125/4)^(4t-3) + R6 000(1 + 0.013125/4)^(4t)

Rearranging the terms gives us: R194 000(1 + 0.013125/4)^(4t) - R6 000(1 + 0.013125/4)^(4t-1) - R6 000(1 + 0.013125/4)^(4t-2) - R6 000(1 + 0.013125/4)^(4t-3) - R200 000(1 + 0.013125/4)^(4t) = 0

Using trial and error, we can solve this equation to find that t = 5.22 years (rounded to 2 decimal places). Therefore, it will take Andrew approximately 5.22 years to settle the loan.

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A. The probability that one selected subcomponent is longer than 122 cm can be found by calculating the area under the normal distribution curve to the right of 122 cm. We can use the z-score formula to standardize the value and then look up the corresponding probability in the standard normal distribution table.

z = (122 - μ) / σ = (122 - 100) / 5.6 = 3.93 (approx.)

Looking up the corresponding probability for a z-score of 3.93 in the standard normal distribution table, we find that it is approximately 0.9999. Therefore, the probability that one selected subcomponent is longer than 122 cm is approximately 0.9999 or 99.99%.

B. To find the probability that the mean length of three randomly selected subcomponents exceeds 122 cm, we need to consider the distribution of the sample mean. Since the sample size is 3 and the subcomponent lengths are normally distributed, the distribution of the sample mean will also be normal.

The mean of the sample mean will still be the same as the population mean, which is 100 cm. However, the standard deviation of the sample mean (also known as the standard error) will be the population standard deviation divided by the square root of the sample size.

Standard error = σ / √n = 5.6 / √3 ≈ 3.24 cm

Now we can calculate the z-score for a mean length of 122 cm:

z = (122 - μ) / standard error = (122 - 100) / 3.24 ≈ 6.79 (approx.)

Again, looking up the corresponding probability for a z-score of 6.79 in the standard normal distribution table, we find that it is extremely close to 1. Therefore, the probability that the mean length of three randomly selected subcomponents exceeds 122 cm is very close to 1 or 100%.

C. If we want to find the probability that all three randomly selected subcomponents have lengths exceeding 122 cm, we can use the probability from Part A and raise it to the power of the sample size since we need all three subcomponents to satisfy the condition.

Probability = (0.9999)^3 ≈ 0.9997

Therefore, the probability that if three subcomponents are randomly selected, all three of them have lengths that exceed 122 cm is approximately 0.9997 or 99.97%.

Based on the given information about the normal distribution of subcomponent lengths, we calculated the probabilities for different scenarios. We found that the probability of selecting a subcomponent longer than 122 cm is very high at 99.99%. Similarly, the probability of the mean length of three subcomponents exceeding 122 cm is also very high at 100%. Finally, the probability that all three randomly selected subcomponents have lengths exceeding 122 cm is approximately 99.97%. These probabilities provide insights into the performance of the automatic machine in terms of producing longer subcomponents.

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Answer:

The end behavior of a function f describes the behavior of the graph of the function at the "ends" of the x-axis. In other words, the end behavior of a function describes the trend of the graph if we look to the right end of the x-axis (as x approaches +∞ ) and to the left end of the x-axis (as x approaches −∞ ).

Step-by-step explanation:

umm....I really hope this helps u

A =
 2   1   1

 1   1   -1

 1   0   1


To construct a 3x3 matrix nonzero matrix such that vector [1 1 -1] is a solution of Ax = 0, A =

 2   1   1

 1   1   -1

 1   0   1.

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Answer:

P(Z < 2.37) = 0.9911.

Step-by-step explanation:

We are given that Let z denote a random variable that has a standard normal distribution.

Let Z = a random variable

So, Z ~ Standard Normal(0, 1)

As we know that the standard normal distribution has a mean of 0 and variance equal to 1.

                          Z  =  \(\frac{X-\mu}{\sigma}\)  ~ N(0,1)

where, \(\mu\) = mean = 0

           \(\sigma\) = standard deviation = 1

Now, the probability that z has a value less than 2.37 is given by = P(Z < 2.37)

        P(Z < 2.37) = P(Z < \(\frac{2.37-0}{1}\) ) = P(Z < 2.37) = 0.9911

The above probability is calculated by looking at the value of x = 2.37 in the z table which has an area of 0.9911.

Answer:

factored form = 4(x−2)(x+3)

Step-by-step explanation:

4 is a factor of the entire equation so factor it out and it will leave U with the answer

To determine the probability that a man and woman getting married both have at least a bachelor's degree, we need to make certain assumptions.

Firstly, we must assume that the probability of a man having at least a bachelor's degree is independent of the probability of a woman having at least a bachelor's degree. Additionally, we must assume that the population of men and women with at least a bachelor's degree is representative of the population of all married couples.
Assuming these conditions are met, we can estimate the probability of a man having at least a bachelor's degree as well as the probability of a woman having at least a bachelor's degree using data from the relevant population. We can then calculate the joint probability of both events occurring simultaneously by multiplying the probabilities of each event. Without data, it is difficult to provide an exact probability. However, according to the U.S. Census Bureau, as of 2019, approximately 35% of the U.S. population aged 25 and older have at least a bachelor's degree. Therefore, assuming that the probabilities are independent, the probability of a man having at least a bachelor's degree is approximately 0.35, and the probability of a woman having at least a bachelor's degree is also approximately 0.35.
Multiplying these probabilities together, we get an estimated probability of 0.1225 or 12.25% chance that a man and woman getting married both have at least a bachelor's degree. However, it's important to remember that this is only an estimate and may not hold true for all populations or regions.

To determine the probability that a man and a woman getting married both have at least a bachelor's degree, we need to make some assumptions and use the concept of probability.
Assumptions:
1. The probability of a man having a bachelor's degree is independent of the probability of a woman having a bachelor's degree.
2. We know the probabilities of a man and a woman having a bachelor's degree in the given population.
Let P(M) be the probability of a man having a bachelor's degree, and P(W) be the probability of a woman having a bachelor's degree. To find the probability of both the man and the woman having a bachelor's degree, we simply multiply these two probabilities:
P(both have bachelor's degree) = P(M) * P(W)
So, the probability that a man and a woman getting married both have at least a bachelor's degree depends on the individual probabilities of a man and a woman having a bachelor's degree in the population under consideration.

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Answer:

Step-by-step explanation:

The first one is equal to.  203/203 is equal to 1.  1 times any number is itself.

The second on is less than.  9/37 is a proper fraction and when a number is multiplied by a proper fraction, it gets smaller.

Answer:

7   1/3

Step-by-step explanation:

Lets do this in steps ok? K!

Important!!!: Look what operation is first in order of operation no parentheses or exponents so division and multiplication is first!

Step 1-- 4 x 7=28

Step 2-- 62 divided by 3 = 20      2/3

Step 3-- 28- 20   2/3

Step 4-- 27   3/3 - 20    2/3= 7    1/3

Hope this helps ∞<3

Answer:

\(-11.3333333333\) \(or\) \(-\frac{34}{3}\) \(or\) \(7\ \frac{1}{3}\)

Step-by-step explanation:

\(--------------------------------------------\)

\(\frac{4\cdot7-62}{3}\) = \(?\)

\(4\cdot7\) = \(28\)

\(\frac{28-62}{3}\) = \(?\)

\(28-62\) = \(-34\)

\(\frac{-34}{3}\) = \(?\)

\(\frac{-34}{3}\) = \(-11.3333333333\) = \(7\ \frac{1}{3}\)

\(--------------------------------------------\)

Hope this helps! <3

\(--------------------------------------------\)

Answer:

x = -6f

Step-by-step explanation:

solve for x by simplifying both sides of the equation, then isolating the variable.

Answer:

\(JL=54\)

Step-by-step explanation:

We are given that K is the midpoint of JL. Using this information, we want to find JL.

By the definition of midpoint, this means that:

\(JK=KL\)

Substitute them for their equations:

\(8x+11=14x-1\)

Solve for x. Subtract 8x from both sides:

\(11=6x-1\)

Add 1 to both sides:

\(6x=12\)

And divide both sides by 6. Hence:

\(x=2\)

JL is the sum of JK and KL. Hence:

\(JK+KL=JL\)

Since JK = KL, substitute either one for the other:

\(JK+(JK)=2JK=JL\)

Substitute JK for its equation:

\(2(8x+11)=JL\)

Since we know that x = 2:

\(2(8(2)+11)=2(16+11)=2(27)=54=JL\)

Thus:

\(JL=54\)

Suppose lnx - lny = y-4 and y is a differentiable function of x. The value of dy/dx when x=4 is 1/4.

To find the value of dy/dx, we can use the given equation and the ln formula to differentiate both sides with respect to x. This will give us:

lnx-lny = y-4

d/dx(lnx-lny) = d/dx(y-4)

1/x-1/y (dy/dx) = dy/dx

(1/x-1/y) dy/dx = 0

dy/dx=(1/x)/(1/y)

dy/dx=y/x

Since we are given that y=4 when x=4, we can substitute these values into the equation to find the value of dy/dx when x=4:

dy/dx=4/4

dy/dx=1/4

Therefore, the value of dy/dx when x=4 is 1/4.

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Answer:

1) m<1=42°

2) m<3=42°

3 m<4=138°

Step-by-step explanation:

1) m<1=180-138=42

2) m<3=180-138=42

3 m<4=138  (Alternate Interior Angle Theorem)

The probability that a randomly chosen point in the circle is outside the inscribed square is 0.360.

The probability is calculated as follows:

Data given:

The diagonal of the square is equal to the diameter of the circle,;

The side length of the square is s

s * √2 = 72

s = 72 / √2

s ≈ 51.02 units

The area of the square:

Area of the square = 51.02 * 51.02

Area of the square ≈ 2604.08 square units

The area of the circle:

Area of the circle = 3.14 * 36 * 36

Area of the circle ≈ 4071.84 square units

Probability = (4071.84 - 2604.08) / 4071.84

Probability ≈ 0.360

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Answer:

x=7

y=10

Step-by-step explanation:

all you do is add 3 to 4, which is 7, so that's x, then add 3 to 7 which is 10, so that's y, and add 3 to 10, which is 13, proving that the numbers for x and y are correct.

hope this helps

Answer:

The cubic function f(x) = x3 is symmetric about the origin (it is an odd function). Here are some types of functions that are odd: Lines Through The Origin – any line with a zero y intercept (b = 0) and a nonzero slope (m not zero) will have equation f(x) = mx.

Step-by-step explanation:

Answer: No

f(x) = x³ + 2x − 5

Step-by-step explanation:

No

f(x) = x³ + 2x − 5

Answer:

Alice

Step-by-step explanation:

If Alice was running 2 miles in 12 minutes then in two hours she would have ran 20 miles. If Jonathan was running 5 miles in 40 minutes then in two hours he would've ran 15 miles. In conclusion Alice would go faster if she was traveling at a constant speed

Answer: 1: Given

2: Distribution

3: Subtraction

4: subtraction

5:division

Step-by-step explanation:

answer:

10:03 am

explanation:

9:00 am + 1 hour (60 min) + 3 min = 10:03 am.

Given

The decay model for the amount of carbon-14 present after t years is,

To find the number of carbon-14 present in 9705 years.

Explanation:

It is given that,

Then, for t=9705,

Hence, the amount of carbon-14 present in 9705 years is 5grams.

Answer:

The answer is 8x-3y hope this helps!

Approximately 33.32% of the students scored higher than Willa on the chemistry exam.

To find the proportion of students who scored higher than Willa, we need to calculate the z-score for her score and then find the corresponding proportion from the standard normal distribution table.

The z-score can be calculated using the formula: z = (x - μ) / σ, where x is Willa's score, μ is the mean, and σ is the standard deviation. Plugging in the values, we get z = (74.8 - 78) / 5 = -0.64.

Looking up the z-score of -0.64 in the standard normal distribution table, we find that the proportion of students who scored higher than Willa is 0.747. However, since we are interested in the proportion above her score, we subtract this value from 1 to get 1 - 0.747 = 0.253, which is equivalent to 25.3%. Therefore, approximately 33.32% of the students scored higher than Willa on the exam

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\(x^2 + 12x=-33 \\ \\ x^2 + 12x+36=3 \\ \\ \boxed{(x+6)^2=3} \\ \\ x+6=\pm \sqrt{3} \\ \\ \boxed{x=-6 \pm \sqrt{3}}\)

Yes its D .............................. Just a Confirmation

Answer:

exponential function

Step-by-step explanation:

geometric sequence

An = A1 * r^(n-1)

common ratio is 2

A1 = 1st term

nagwa

mthway